Wurdeman graduated from the University of Washington program in Architecture in 1927 with a Bachelor of Architecture degree (B.Arch.). After graduation he apprenticed with the Seattle firm Bebb and Gould and participated in design of the Seattle Art Museum (now Seattle Asian Art Museum) in Seattle's Volunteer Park.
Wurdeman had moved to Los Angeles by 1933 and formed a partnership with his University of Washington classmate Welton Becket and local architect Charles F. Plummer. The Moderne Pan-Pacific Auditorium, dating from 1935, brought them local fame. Subsequent commissions included residences for James Cagney, Robert Montgomery, and other film celebrities.
After Plummer died in 1939, the surviving partners renamed the firm Wurdeman and Becket. The firm was responsible for Bullock's Pasadena (1944) and several corporate headquarters. Wurdeman and Becket practiced "total design", taking responsibility for master planning, engineering, interiors, fixtures and furnishings, landscape, and graphics.
After Wurdeman's death in 1949, Becket carried on the practice alone as Welton Becket Associates.